CF1003D.Coins and Queries

Polycarp has $n$ coins, the value of the $i$ -th coin is $a_i$ . It is guaranteed that all the values are integer powers of $2$ (i.e. $a_i = 2^d$ for some non-negative integer number $d$ ).

Polycarp wants to know answers on $q$ queries. The $j$ -th query is described as integer number $b_j$ . The answer to the query is the minimum number of coins that is necessary to obtain the value $b_j$ using some subset of coins (Polycarp can use only coins he has). If Polycarp can't obtain the value $b_j$ , the answer to the $j$ -th query is -1.

The queries are independent (the answer on the query doesn't affect Polycarp's coins).

The first line of the input contains two integers $n$ and $q$ ( $1 \le n, q \le 2 \cdot 10^5$ ) — the number of coins and the number of queries.

The second line of the input contains $n$ integers $a_1, a_2, \dots, a_n$ — values of coins ( $1 \le a_i \le 2 \cdot 10^9$ ). It is guaranteed that all $a_i$ are integer powers of $2$ (i.e. $a_i = 2^d$ for some non-negative integer number $d$ ).

The next $q$ lines contain one integer each. The $j$ -th line contains one integer $b_j$ — the value of the $j$ -th query ( $1 \le b_j \le 10^9$ ).

Print $q$ integers $ans_j$ . The $j$ -th integer must be equal to the answer on the $j$ -th query. If Polycarp can't obtain the value $b_j$ the answer to the $j$ -th query is -1.